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Gradients of Risk Measures: Theory and Application to Catastrophe Risk Management and Reinsurance Pr
Year Of Publication: 2004
Month Of Publication: March
Pages: 44
Download Count: 811
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Comment Num: 0
Language: EN
Who Can Read: Free
Date: 11-2-2004
Publisher: Administrator
As part of pricing, many reinsurers would like to know the incremental impact that adding a new contractor canceling an existing contract might have on the capital needed to support the entire portfolio ofbusiness. Typically, catastrophe models take hours or days to run, ruling out a straightforward approach. Amethod of assessing incremental impact which did not require repeatedly simulating losses to the entireportfolio would therefore be quite useful. Efficient procedures for calculating the first derivatives ofwidely-used risk measures (such as Value at Risk and Tail Value at Risk) with respect to portfolioparameters would support the development of such a method. This paper presents general formulas forgradients of risk measures including VaR and TVaR. While the derivative of VaR in the case of linear riskmodels is widely known, this paper presents the general solution applicable not only to linear portfolioweights, but also to nonlinear parameters, such as retentions and limits. Implementation of the theoreticalformulas within existing catastrophe simulation models is elaborated. A normal mixture approximationleads to a closed form solution for the incremental impact on VaR or TVaR of adding or removing acontract from a portfolio of excess-of-loss contracts.
Major, John Sign in to follow this author
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